It's a valid criticism. After reading the Companion books, it's really apparent how much of the story is just sort of made up as we go. The writing team does an awesome job of tying everything together to the main plot, but we know that the angel storyline was an invention of the spring of 2008, and that the Trickster really was just a Trickster in his first appearances.
That being said, I'm going to explain how the Psychic Kids DO make sense....
What it hinges on is how much Lucifer's side KNEW. You have to think of it in terms of prophecy. This is how I picture it:
1. There is a prophecy that there will be two siblings - one of which will have demon-blood. One sibling will be Lucifer's vessel, the other will be Michael's. They'll bring about the apocalypse. This is what I picture Lucifer telling Azazel in the convent in 1972 - "You must find me a child. A very special child..." BUT he can't pinpoint how to find this child.
2. So, the trick is, Azazel didn't know WHICH child. He didn't have a name or gender or place or parentage...so he went about the country (the world? Maybe Luci was able to narrow it down to the continental USA) making deals with potential parents that
3. Of course, this meant that he ended up with multiple "special children" - how do you tell which one is the right one? Well, if the prophecy is to be fulfilled, and if he lucked out and actually found the correct child, then destiny would favour the survival of that child over the others...so, let's have them battle to the death - whoever is left standing might not be the correct kid, but it'd certainly weed out the kids who DEFINITELY aren't correct.
4. Get that kid to open the gate to Hell so that Lilith can get loose - because eventually she has to be killed.
5. Get that kid to lead a demon army to break the seals, right after you get Alistair to make a righteous man spill blood in hell....John Winchester not working out? No problem, Dean just made a deal, wait a year to get the ball rolling...your victorious special kid refusing to take up the his position as leader of a seal-breaking demon army? Get a demon to infiltrate his personal relationships, gain his trust through false promises, maybe get him hooked on drugs so that his brain gets a bit muddled, convince him that he's helping the world when he's really not and....
6. Bam! Seals are broken, Lucifer rises, and if he were alive Azazel would be kicking back and congratulating himself on a job well done - after all, he did find the right kid after all...he knew there was something off about that Jake guy.
Anyway, that's how I see it all happening. I'm not sure if the writers will ever address the issue, so I just thought I would put my version events out there.